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A mathematical model for cell differentiation, as an evolutionary and regulated process.

Authors
  • Prokharau, Pavel A1
  • Vermolen, Fred J
  • García-Aznar, José Manuel
  • 1 a Delft Institute of Applied Mathematics, Delft University of Technology , HB 07.290, Mekelweg 4, 2628 CD , Delft , The Netherlands. , (Netherlands)
Type
Published Article
Journal
Computer Methods in Biomechanics & Biomedical Engineering
Publisher
Informa UK (Taylor & Francis)
Publication Date
Aug 01, 2014
Volume
17
Issue
10
Pages
1051–1070
Identifiers
DOI: 10.1080/10255842.2012.736503
PMID: 23113617
Source
Medline
License
Unknown

Abstract

We introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitrary number of parameters. In the current approach, cell differentiation is modelled by means of a differentiation state variable. Cells are assumed to differentiate into an arbitrary number of cell types. The differentiation path is considered as reversible, unless differentiation has fully completed. Cell differentiation is incorporated into the partial differential equations (PDEs), which model the tissue regeneration process, by means of an advection term in the differentiation state space. This allows one to consider the differentiation path of cells, which is not possible if a reaction-like term is used for differentiation. The boundary conditions, which should be specified for the general PDEs, are derived from the flux of the fully non-differentiated cells and from the irreversibility of the fully completed differentiation process. An application of the proposed model for peri-implant osseointegration is considered. Numerical results are compared with experimental data. Potential lines of further development of the present approach are proposed.

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